Problem $1$: Collusive Monopsony. There are two teams that produce hockey games.

For simplicity, call them team $1$ and team $2.$ Each team is a monopoly in their product

market with inverse demand curve:

P $($q$)=1081/2$q

The production function for each team is given by:

q$()=2$ where $$ is the quantity of labor hired by the team. The aggregate supply of labor is: w$($L$)=60+3$L where L $=1+2$ is the total amount of labor hired by the two teams.

$1.$ Assume that the two teams compete against one another by simultaneously choosing the quantity of labor to hire. This is the oligopsony case we$$ve discussed in class. The two teams are not cooperating$$they are best responding to each other.

a$)$ Write out the profit function for team $1.$ In your final expression, your $1$ should be an expression of $1$ and $2.$

b$)$ Find each team$$s best response function. $($Hint: $1$ as a function of $2,$ and $2$ as a function of $1)$

c$)$ Use symmetry to solve for the equilibrium amount of labor chosen by each team $().$

d$)$ What is the equilibrium wage $($w$)?$

e$)$ What is the profit for each team $($n$)?$

$2.$ Now, assume that the two teams collude as a $($monopsony$)$ league. This is the single$-$

period collusive monopsony example we$$ve discussed in class.

a$)$ Find the aggregate product demand curve for the league. I am looking for the

inverse demand curve here. $($Hint: you need to aggregate the two teams$$ product

demand curves$)$

b$)$ What is the new equilibrium amount of labor in the market $($L$)?($Hint: use the

optimality condition M F C $=$ M RPL that we discussed in class$)$

$1$

c$)$ What is the new equilibrium wage $($w$)?$

d$)$ How much labor is hired by each team $()?($Hint: symmetry.$)$

e$)$ What is the profit for each team under this collusive scheme $($c$)?$

$3.$ Imagine that team $1$ deviates from the collusive agreement while team $2$ keeps choos$-$

ing the collusive amount of labor. Assume that team $1$ no longer views team $2$ as a partner, but as a rival.

a$)$ Given team $2$s choice of labor amount, how much labor should team $1$ hire to maximize profits $(1)?($Hint: team $1$ utilizes its best response function.$)$

b$)$ What is the total amount of labor being hired in the market $($L$)?$

c$)$ What is the corresponding wage level $($w$)?$

d$)$ What are team $1$s profits from deviating $($d$)?$

e$)$ Find the cutoff value $$ such that, as long as the discount factor $>$$,$ then collusion is sustainable as an equilibrium of the infinitely$-$repeated game